Question 1158324
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original response deleted... I'm looking at this further....<br>
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In my earlier attempt at solving this, I tried to simplify the problem by treating all the percent increases and decreases as being relative to the original price.  That way, for instance,  increases of 3% and 3% would exactly balance decreases of 1%, 2%, and 3%.<br>
However, that is probably not how the problem was intended.<br>
If the percentage increases or decreases are treated as multipliers, there is NO permutation of 5 of the 6 posssible percentage changes that results in an ending price exactly equal to the starting price.<br>
So I looked at the problem again....<br>
Certainly the other tutor missed the point of the problem, finding the percent increase or decrease if each of the changes is applied once.<br>
It appears to me that a purely analytic solution would be extremely tedious, making it necessary to examine each permutation of 5 of the 6 percentage changes.<br>
So I built an excel spreadsheet with all 6^5=7776 permutations of 5 of the 6 and identified the ones that produced a product greater than 1.<br>
ANSWER: 3588 of the 7776 permutations of 5 of the 6 percentage changes produce a product greater than 1.  Therefore, the probability that the stock price will be above the original $10 after 5 days is 3588/7776, or about 46.142%.<br>